Traffic demands are growing with deployments of mobile communication systems for the 5th generation and beyond., which is further accelerated by the pandemic [1]}.
Optical fiber communications take a key role in the communication infrastructure because of its high capacity. In the past, the modulation formats used in optical fiber communications were binary, e.g., on–off keying, binary, or quaternary phase-shift keying without forward error correction (FEC) or with hard-decision FEC [2]}. However, the latest 400 Gb/s standards [3]}, [4]} utilize 16-ary quadrature amplitude modulation (QAM) with soft-decision (SD) FEC under bit-interleaved coded modulation (BICM)[5]}, [6]}, [7]}, [8]}. Furthermore, constellation shaping [9]}, or more specifically, probabilistic shaping (PS) [10]}, [11]}, has attracted wide research interest due to its capacity-approaching performance [12]}, [13]}, [14]}, [15]}. Especially reverse concatenation, where the shaping encoding (also known as distribution matching, DM)[16]}, [17]}, [18]}, [19]}, [20]}, [21]}, is done outside the FEC encoding [22]}, [23]}, [24]}, made PS deployable in terms of implementation capability.
